Why: To keep traffic moving.
You can turn right on Red if,
There are no pedestrians in the crosswalk,
There are no on coming cars from the left,
The left turn lane on the the opposite side does not have a green arrow,
There is no sign prohibiting a right hand turn on red, and
There is no green right arrow.
A green right arrow indicate no right turn on red.

7-13-2017 But you asked why. It is because the federal government wants consistent driving laws in all states, and they decreed that right on red after stopping is ok unless there is some reason to forbid it.

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